1. Field of the Invention
The present invention relates to the recovery of 3D cardiac motion from a volunteer dataset of tagged MR images and more specifically to a system that includes global models with parametric offsets, constant volume constraints for cardiac motion recovery and tessellation of the model.
2. Description of the Prior Art
Different forms of hybrid models have been described in vision literature over the past several years. The following will focus only on those models most closely related to the present invention. In the models related to the present invention, the global component has been described by a parametric model or as a series of vibrational modes. Parametric models are described by D. Terzopoulos and D. Metaxas in "Dynamic 3D Models With Local And Global Deformations: Deformable Superquadrics", IEEE PAMI, 13 (7):703-714, 1991; by J. Park, D. Metaxas and L. Axel in "Volumetric Deformzible Models With Parametric Functions: A New Approach To The 3D Motion Analysis Of The LV From MRI-SPAMM", Proceedings of the 5th IEEE ICCV, MIT, Mass., pages 700-705, 1995; and by J. Park, D. Metaxas and A. Young in "Deformable Models With Parameter Functions: Application To Heart Wall Modeling", Proceedings of the IEEE CVPR, Seattle, Wash., pages 437-442, 1994. Vibrational modes are described by A. Pentland in "The Thingworld Modeling System: Virtual Sculpting By Modal Forces", Proceedings of SIGGRAPH, pages 143-144, 1990; and by B. C. Vemuri and A. Radisavljevic in "From Global To Local, A Continuum Of Shape Models With Fractal Priors", IEEE CVPR, pages 307-313, 1993.
A. Pentland and J. Williams in "Good Vibrations: Modal Dynamics For Graphics And Animation", Computer Graphics, 23(3):215-222, July 1989, presented the first use of hybrid modeling in the programming environment, ThingWorld. The system coupled a global geometric modal representation with a local description of the object's dynamics.
Terzopoulos and Metaxas included a global superquadric component in their deformable model. The deformations from this base superquadric model take( the form of a thin membrane spline described using the Finite Element Method (FEM). Unlike Pentland's model, th(e underlying superquadric as well as the spline mesh deformed to fit the data.
Park, Metaxas and Young developed a thick ellipsoidal model for recovering 3-D cardiac motion from tagged-MR data. Their model, developed independently and in parallel with T. O'Donnell, A. Gupta and T. Boult in "The Hybird Volumetric Ventriculoid: A model For MR-SPAMN 3-D Analysis", Proceedings of Computers in Cardiology, IEEE, 1995, provided a piecewise plot of the change in relevant global LV characteristics. The.Lr model, however, does not report strain and is recovered under the unrealistic assumption that the tag columns remain straight over the cardiac cycle. Their modiel formulation differs from the model formulation of the present invention in the following ways. First, their model does not have distinct global and local components. They use linear piecewise parametric functions to express local deformations. Second, the default shape of the model is a thick ellipsoid rather than a shape closer to a real LV. Third, their model does not provide a concise description of the LV movement. Rather, piecewise plots describe the motion. Fourth, their model assumes a dense tag acquisition and therefore makes no use of "regularizing" constraints.
O'Donnell, Gupta, and Boult presented a thick superelliptic model, the HVV. While there is a clear distinction between global and offset components in this model, it differs from the approach of the present invention in that the offsets are not parametric. In addition, the model fitting was influenced via an internodal stretching penalty as opposed to current constant volume constraint of the present invention.
W. O'Dell, C. Moore, W. Hunter, E. Zerhouni and E. McVeigh in "Displacement Field Fitting For Calculating 3D Myocardial Deformations From Tagged MR Images", Radiology, 195:829-835, 1995, recovered 3-D cardiac motion using a prolate spheroidal model. The coefficients of their series expansion do not, however, give an intuition as to the shape and movement of the LV. Also, their tags image as a series of parallel line(s rather than a 2-D grid, inviting the aperture problem.
Finally, T. Denny and J. Prince in "3D Displacement Field Reconstruction From Planar Tagged Cardiac MR Images", Proceedings of the IEEE Workshop on Biomedical Image Analysis, pages 51-60, 1994, employed a multidimensional stochastic model for measuring cardiac motion from tagged-MR images. They used the Fisher estimation framework to approximate the movement of the LV from sparse displacement measurements with cons-ant volume constraints.